# American Institute of Mathematical Sciences

doi: 10.3934/eect.2020005

## The Kalman condition for the boundary controllability of coupled 1-d wave equations

 1 Dept. of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USA 2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, G. U. 04510 D.F., México

Received  December 2018 Revised  March 2019 Published  August 2019

The focus of this paper is the exact controllability of a system of $N$ one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman condition (necessary and sufficient) and give a description of the attainable set. In general, this set is not optimal, but can be refined under certain conditions.

Citation: Sergei Avdonin, Jeff Park, Luz de Teresa. The Kalman condition for the boundary controllability of coupled 1-d wave equations. Evolution Equations & Control Theory, doi: 10.3934/eect.2020005
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